A103546 Decimal expansion of the negated value of the smallest real root of the quintic equation x^5 + 2*x^4 - 2*x^3 - x^2 + 2*x -1 = 0.

2, 4, 8, 6, 3, 4, 3, 7, 6, 4, 9, 5, 9, 0, 7, 9, 6, 6, 5, 2, 6, 7, 1, 9, 5, 3, 3, 0, 9, 7, 0, 7, 2, 2, 1, 2, 0, 1, 4, 0, 9, 0, 3, 8, 5, 2, 5, 9, 2, 7, 0, 5, 8, 1, 9, 7, 6, 4, 9, 9, 4, 0, 3, 3, 2, 9, 9, 1, 1, 1, 8, 5, 4, 0, 0, 1, 1, 4, 7, 3, 0, 5, 5, 1, 5, 5, 9, 0, 9, 1, 0, 4, 6, 9, 2, 8, 0, 8, 0, 1, 7, 2, 3, 1, 7

Offset: 1

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Mar 23 2005

Keywords

• cons
• nonn

Comments

This is an approximation to the Feigenbaum reduction parameter.

The other two real roots are 0.76660865407289... and -1.16317291980104...

Examples

			The real roots are (roughly) -2.486343765, -1.163172920, 0.7666086541.
		

Links

• Eric Weisstein's World of Mathematics, Feigenbaum Constant.
• Index entries for algebraic numbers, degree 5

Crossrefs

Cf. A006891, A103616.

Programs

Mathematica

RealDigits[ FindRoot[x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1 == 0, {x, -3}, WorkingPrecision -> 2^7][[1, 2]]][[1]] (* Robert G. Wilson v, Mar 26 2005 *)
Root[#^5 + 2#^4 - 2#^3 - #^2 + 2# - 1&, 1] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 27 2013 *)

PARI

polrootsreal(x^5 - 2*x^4 - 2*x^3 + x^2 + 2*x + 1)[3] \\ Charles R Greathouse IV, Apr 14 2014